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Question

Calculate the inductance of a unit length of a double tape line as shown in figure. The tapes are separated by a distance h which is considerably less than their width b.


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Solution

Step 1: Given data

Distance = h

Width = b

Step 2: Concept used

By using Maxwell's ampere law, B=μ0I2b

where,

B is the magnetic field.

μ0 is the permeability of free space(4π×10-7N/A2).

I is the current.

b is the width of the given double tape.

ϕ=2BA

Step 3: Calculation of inductance of unit length

B×dl=μ0I

B×2b=μ0I

B=μ0I2b

Step 4: Find the magnetic flux

Since, net field = 2B Magnetic flux passing through this double tape

ϕ=2BA

=2B(1h)

ϕ=μ0Ib1h

Then, inductance(L)=ϕI

=μ01hb

=L1

=μ0hB

Therefore, the inductance of unit length is μ0hB.


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